Method for generating and detecting marks

ABSTRACT

Methods ( 450, 750 ) are disclosed for embedding a watermark into an image ( 400, 700 ). The watermark comprises at least one basis pattern. A real part of the basis pattern(s) ( 410, 710 ) is added to the image ( 400, 700 ) to form a watermarked image ( 420, 730 ). The basis pattern(s) has scale and rotation invariant properties. The pattern(s) is preferably added to the image at a low intensity to make the pattern(s) invisible or imperceptible to the human visual system under normal viewing conditions. Methods ( 800, 900 ) are also disclosed for detecting a watermark from a watermarked image ( 810, 910 ). The watermark image ( 810, 910 ) is correlated with the basis pattern to provide a result image ( 830, 950 ). Peaks in the result image ( 830, 950 ) correspond with positions where the basis pattern was detected in the watermarked image ( 830, 950 )

TECHNICAL FIELD OF THE INVENTION

[0001] The present intention relates to the generation, embedding anddetection of patterns in images, audio streams, video, and documents orsurfaces of articles. Such embedded patterns may be used for invisiblewatermarking, and/or for alignment information. In particular, thepresent invention relates to embedded patterns that have scale androtation invariant properties.

BACKGROUND ART

[0002] With the advent of digital images and digital image distributionsprotection of such digital images against unauthorised copying hasbecome an issue for image publishers and authors One technique used toidentify the ownership of an image is to embed a pattern or patternsinto the image, such that the embedded pattern is not visible to thenaked eye of an observer. Such a pattern is called a watermark. Thepresence of the watermark can be detected in the copied image by theowner of the original image, thereby proving their ownership.

[0003] Systems are known for embedding a pattern or patterns into animage or document. However, present methods of invisible watermarking ofdocuments and images are often very sensitive, therefore not robust, togeometric image distortions. The most common image distortions arechanges in the magnification or scaling, changes to the orientation ofthe image or rotation, and losing edge information of the image orcropping.

[0004] Known methods which are robust to such changes, are eitherincapable of storing significant amounts of data in the watermark, orare susceptible to malicious intervention for the reason that thepattern is easily detected by simple spectral methods. One such spectralmethod is an analysis of the Fourier magnitude peaks of the image withan embedded watermark.

[0005] One of the most popular and effective methods for detectingpatterns is correlation. In fact, for linear systems, correlation, ormatched filtering, can be shown to be mathematically an optimaldetection method. Unfortunately correlation in two dimensions is not, ingeneral, invariant with orientation or scaling.

[0006] It should be noted that correlation can only give well definedand easily distinguished correlation magnitude peaks if the underlyingpattern has a broad Fourier magnitude distribution. This is aconsequence of the uncertainty principle. Therefore, patterns with verysharp or constrained Fourier magnitudes, such as a narrow-bandpassfunction, are ill equipped for correlation purposes.

[0007] Rotation invariance in known systems is typically achieved byusing circular symmetric patterns. Alternatively the correlation can berepeated many times with the test pattern at many differentorientations, so that at least one correlation is close to the actualorientation. Scale related problems are usually solved by repeatedcorrelations at many different scales so that at least one correlationis close to the actual scale. Such methods are impractical, and as aconsequence correlation seldom is used in cases when arbitrary rotationand/or scaling is present.

DISCLOSURE OF THE INVENTION

[0008] It is an object of the present invention to substantiallyovercome, or at least ameliorate, one or more disadvantages of existingarrangements.

[0009] According to a first aspect of the invention, there is provided amethod of embedding a watermark into an image, said method comprisingthe step of:

[0010] maintaining at least one basis pattern; and

[0011] adding said basis pattern(s) to said image, said basis pattern(s)being formed substantially from a basis function, wherein said basisfunction is defined such that said basis function when correlated with ascaled and rotated version of said basis function is substantially equalto the auto-correlation of said function within a complex multiplicativeconstant.

[0012] According to a second aspect of the invention, there is provideda method of detecting a watermark from an image, said watermark having afirst basis pattern embedded, said method comprising the steps of:

[0013] maintaining a second basis pattern; and

[0014] detecting said first basis pattern in said image using saidsecond basis pattern, said first and second basis patterns being formedsubstantially from a basis function, wherein said basis function isdefined such that said basis function when correlated with a scaled androtated version of said basis function is substantially equal to theauto-correlation of said function within a complex multiplicativeconstant.

[0015] According to a third aspect of the invention, there is provided amethod of adding registration marks to an image, said method comprisingthe step of:

[0016] maintaining at least one basis pattern, said basis pattern(s)being formed substantially from a basis function, wherein said basisfunction is defined such that said basis function when correlated with ascaled and rotated version of said basis function is substantially equalto the auto-correlation of said function within a complex multiplicativeconstant;

[0017] adding said basis pattern(s) to said image at at least threepredetermined offsets relative to a center of said image.

[0018] According to a fourth aspect of the invention, there is provideda method of registering a transformed image, wherein a first basispattern is embedded in said image before transformation at at leastthree predetermined positions, said method comprising the steps of:

[0019] maintaining a second basis pattern;

[0020] detecting said first basis pattern in said transformed imageusing said second basis pattern, said first and second basis patternsbeing formed substantially from a basis function, wherein said basisfunction is defined such that said basis function when correlated with ascaled and rotated version of said basis function is substantially equalto the auto-correlation of said function within a complex multiplicativeconstant;

[0021] comparing positions of said first pattern with said predeterminedpositions;

[0022] determining linear transformations for transforming saidpositions of said first pattern with said predetermined positions; and

[0023] transforming said image to invert said linear transformations.

[0024] According to a fifth aspect of the invention, there is provided amethod of embedding a watermark into an audio stream, said methodcomprising the step of:

[0025] maintaining at least one basis pattern; and

[0026] adding said basis pattern(s) to said audio stream, said basispattern(s) being formed substantially from a basis function, whereinsaid basis function is defined such that said basis function whencorrelated with a scaled version of said basis function is substantiallyequal to the auto-correlation of said function within a complexmultiplicative constant.

[0027] According to a sixth aspect of the invention, there is provided amethod of detecting a watermark from an audio stream, said watermarkhaving a first basis pattern embedded, said method comprising the stepsof:

[0028] maintaining a second basis pattern; and

[0029] detecting said first basis pattern in said audio stream usingsaid second basis pattern, said first and second basis patterns beingformed substantially from a basis function, wherein said basis functionis defined such that said basis function when correlated with a scaledversion of said basis function is substantially equal to theauto-correlation of said function within a complex multiplicativeconstant.

[0030] According to yet another aspect of the invention, there isprovided an apparatus for implementing any one of the aforementionedmethods.

[0031] According to yet another aspect of the invention there isprovided a program stored in a memory medium for implementing any one ofthe methods described above.

BRIEF DESCRIPTION OF THE DRAWINGS

[0032] A number of embodiments of the present invention will now bedescribed with reference to the drawings, in which:

[0033]FIG. 1 shows a section of a scale invariant function;

[0034]FIGS. 2A and 2B show the real and imaginary parts of a logarithmicradial phase function having an annular region defined by minimum andmaximum radii;

[0035]FIGS. 3A and 3B show the real and imaginary parts of a logarithmicradial harmonic phase function;

[0036]FIG. 4 shows a schematic diagram of a process of watermarking animage;

[0037]FIG. 5 shows an example watermark pattern;

[0038]FIG. 6 shows an example image with the watermark pattern of FIG. 5embedded using the process of FIG. 4;

[0039]FIG. 7A shows a schematic diagram of an alternative process ofwatermarking an image using de-emphasis;

[0040]FIG. 7B shows the example image with the watermark pattern of FIG.5 embedded using the process of FIG. 7A;

[0041]FIG. 8 shows a schematic diagram of a process of detecting awatermark in an image;

[0042]FIG. 9 shows a schematic diagram of an alternative process ofdetecting a watermark in an image using emphasis;

[0043]FIG. 10A shows the magnitude image of correlating the image ofFIG. 6 with the correct pattern using the detection process of FIG. 8;

[0044]FIG. 10B shows details of one of the magnitude peaks of FIG. 10A;

[0045]FIG. 11A shows the magnitude image of correlating the image ofFIG. 7B with the correct pattern using the detection process of FIG. 9;

[0046]FIG. 11B shows details of one of the magnitude peaks of FIG. 11A;

[0047]FIG. 12 shows the example image of FIG. 6 rotated, scaled andcropped;

[0048]FIG. 13 shows the result of correlating the image of FIG. 12 withthe correct pattern using the detection process of FIG. 9;

[0049]FIG. 14 shows details of one of the magnitude peaks of FIG. 13;

[0050]FIG. 15 shows a schematic block diagram of a system;

[0051]FIG. 16A shows the real part of an example a logarithmic radialphase function restricted within a subregion having an arbitrary shape;

[0052]FIG. 16B shows the intensity of a correlation magnitude peak as aresult of correlating a square LRHF with a circular complex LRHF; and

[0053]FIG. 16C shows the intensity of the correlation magnitude peak asa result of correlating the arbitrarily shaped LRHF shown in FIG. 16Awith a circular complex LRHF.

DETAILED DESCRIPTION

[0054] Basic properties of a group of functions, including theircorrelation properties, will first be described. Processes forwatemarking, watermark detection, and apparatus follows the descriptionof the basic properties of those functions.

[0055] Certain functions have a scale invariant property, whereby achange of scale in the coordinate results in a transformed function thatis the same as the original functions apart from a multiplicativeconstant. These functions are sometimes referred to as homogeneousfunctions. Consider a homogeneous function:

ƒ(γ)=cos[α1n(γ)]  (1)

[0056] having a logarithmic phase as follows:

ψ(γ)=α1n(γ)  (2)

[0057] Such a phase has a frequency of$\frac{\psi}{r} = {\frac{\alpha}{r}.}$

[0058] The function ƒ(γ) has the useful scaling property, in that:

ƒ(αγ)=cos [α1n(αγ)]=cos[α1n(γ)+α1n(α)]  (3)

[0059] In other words, a coordinate scale change only produces a fixedphase change in the cosine. The function in Equation (1) has somepeculiar properties, such as an infinite number of periods in the range0≦γ<ε, and the phase approaches as the radius tends to zero. Theundesired effects of these properties can be largely avoided by removalof a central region below a threshold radius. FIG. 1 shows aone-dimensional example of a simple oscillating homogeneous functionhaving the form of Equation (1), for values 0.01≦x≦1.

[0060] The homogeneity condition can also be viewed as a self-similaritycriterion. Self-similar functions produce correlation magnitude peakseven when one of the correlated functions is resealed. A complexfunction with the self-similarity property is:

ƒ_(α)(γ)=γ^(ρ)exp[iα1n(γ)]  (4)

[0061] A scale change provides:

ƒ_(α)(αγ)=α^(ρ)γ^(ρ)exp[iα1n(γ)]exp[iα1n(α)]=α^(ρ)exp[iα1n(α)]ƒ_(α)(γ)  (5)

[0062] which introduces a magnitude and phase change. By using a complexexponent:

exp[iα1n(γ)]=γ^(iα)  (6)

[0063] Equation (4) can be written as:

ƒ_(α)(γ)=γ^(ρ+1α)  (7)

[0064] Equation (7) represents a family of functions, which have aperiodic radial structure. FIGS. 2A and 2B show the real and imaginaryparts of a pattern having the form of Equation (7) where a polardistance γ is defined in terms of the Cartesian axes as γ²=x²+y² and inwhich values of r≦R₁ has been removed to avoid aliasing. The complexfunction ƒ_(α)(γ) has negative values. Therefore, for the functionƒ_(α)(γ) to be displayed, the values the function ƒ_(α)(γ) have beennormalised around a value of 127, with all values ranging from 0 to 255,with 0 representing black, 255 representing white, and intermediatelevels representing levels of grey.

[0065] Functions of the form of Equation (7) have some usefulorthogonality properties over an annular region, with the annular regiondefined by a maximum radius R₂ and the minimum radius R₁. Consider theradial function:

ƒ_(m)(γ)=γ^(ρ)γ^(1α.)  (8)

[0066] The correlation at the origin, or zero shift, is defined by anoverlap integral I_(min) of this function ƒ_(m)(γ) with another similarfunction ƒ_(n)(γ) with parameter α_(n) instead of parameter α_(m), andcan be written in polar coordinates as: $\begin{matrix}{I_{mn} = {{\int_{R_{1}}^{R_{2}}{2\pi \quad {{rf}_{m}(r)}{f_{n}^{*}(r)}\quad {r}}} = \frac{2{\pi \left( {{R_{2}^{{2p} + 2}R_{2}^{i{({\alpha_{m} - \alpha_{n}})}}} - {R_{1}^{{2p} + 2}R_{2}^{i{({\alpha_{m} - \alpha_{n}})}}}} \right)}}{{2p} + 2 + {i\left( {\alpha_{m} - \alpha_{n}} \right)}}}} & (9)\end{matrix}$

[0067] From Equation (9), it can be seen that a prerequisite oforthogonality of the functions ƒ_(m)(γ) and ƒ_(n)(γ), is that p=−1. Forone-dimensional functions, the orthogonality prerequisite is p=−½.

[0068] Generally, the magnitude squared of the overlap integral|I_(min)|² may be written as a sinc function as follows: $\begin{matrix}{{I_{mn}}^{2} = \frac{\left( {4\pi} \right)^{2}{\sin^{2}\left( {{\frac{1}{2}\left\lbrack {\alpha_{m} - \alpha_{n}} \right\rbrack}{\ln \left\lbrack {R_{2}/R_{1}} \right\rbrack}} \right)}}{\left( {\alpha_{m} - \alpha_{n}} \right)^{2}}} & (10)\end{matrix}$

[0069] The magnitude of the overlap integral |I_(min)| is a maximum asthe parameters α_(n) and α_(m) approach α_(n)−α_(m)=0 , and zero when$\begin{matrix}{{{\alpha_{m} - \alpha_{n}} = \frac{2\pi \quad j}{\ln \left\lbrack {R_{2}/R_{1}} \right\rbrack}},{j = {integer}},{{{but}\quad j} \neq 0}} & (11)\end{matrix}$

 j=integer, but j≢0  (11)

[0070] In practice, the magnitude of the overlap integral |I_(min)| issmall or negligible when $\begin{matrix}{{{\alpha_{m} - \alpha_{n}}} > \frac{2\pi}{\ln \left\lbrack {R_{2}/R_{1}} \right\rbrack}} & (12)\end{matrix}$

[0071] The above condition is an approximate orthogonality condition,useful for estimation purposes. In practice the ratio R₂/R₁ is chosen tobe of the order 2 to 4, so that ln(R₂/R₁)≈1.

[0072] By including a spiral phase function in Equation (8), therebycausing polar angle θ=tan⁻¹[y/x] variations in the pattern function, itcan be shown that the pattern function retains its scale invariant andorthogonality properties. Consider a scale and rotation invariantpattern g, which has a circular harmonic phase defined by the parameterk, where parameter k is an integer. Such a function is sometimesreferred to as a logarithmic radial harmonic function [LRHF], and hasthe form:

g _(mk)(γ,θ)=γ^(ρ)γ^(lα,)e^(ikθ)  (13)

[0073] The overlap integral I_(mknl) of this LRHF g_(nlk)(γ, θ) withanother similar LRHF g_(nl)(γ, θ) with parameters α_(n) and k, over anannular region, is: $\begin{matrix}{I_{mknl} = {{\int_{- \pi}^{+ \pi}{\int_{R_{1}}^{R_{2}}{2\pi \quad {{rg}_{mk}(r)}{g_{nl}^{*}(r)}\quad {r}\quad {\theta}}}} = {2\pi {\int_{- \pi}^{+ \pi}{^{{i{({k - l})}}\theta}{\theta}{\int_{R_{1}}^{R_{2}}{r^{{2p} + 1}r^{i{({\alpha_{m} - \alpha_{n}})}}\quad {r}}}}}}}} & (14)\end{matrix}$

[0074] As is evident from Equation (14), the overlap integral I_(mknl)is simple to calculate because of the radial/tangential separability.Equation (14) can be further simplified because the tangential componentintegrates to a Kronecker delta function as follows: $\begin{matrix}{{\int_{- \pi}^{+ \pi}{^{{i{({k - l})}}0}{\theta}}} = {{2{\pi\delta}_{kl}} = \left\{ \begin{matrix}{2\pi} & {,{k = l}} \\0 & {,{k \neq l}}\end{matrix} \right.}} & (15)\end{matrix}$

[0075] causing the overlap integral I_(mknl) to simplify to$\begin{matrix}{I_{mknl} = {\left( {2\pi} \right)^{2}\delta_{kl}\frac{\left( {{R_{2}^{{2p} + 2}R_{2}^{i{({\alpha_{m} - \alpha_{n}})}}} - {R_{1}^{{2p} + 2}R_{1}^{i{({\alpha_{m} - \alpha_{n}})}}}} \right)}{{2p} + 2 + {i\left( {\alpha_{m} - \alpha_{n}} \right)}}}} & (16)\end{matrix}$

[0076] Again, at orthogonality where p=−1, the magnitude squared of theoverlap integral is: $\begin{matrix}{{I_{mknl}}^{2} = {\left( {4\pi} \right)^{2}\delta_{kl}\frac{\sin^{2}\left( {{\frac{1}{2}\left\lbrack {\alpha_{m} - \alpha_{n}} \right\rbrack}{\ln \left\lbrack {R_{2}/R_{1}} \right\rbrack}} \right)}{\left( {\alpha_{m} - \alpha_{n}} \right)^{2}}}} & (17)\end{matrix}$

[0077] The preceding analysis refers to complex exponential functions,but in practice, images are limited to real, as well as positive,reflectivity, transmissivity, or intensity values. It can be shown thatif the overlap integral I_(mknl) is calculated for the real part of oneLRHF g_(mk) with a full complex LRHF g_(nl), a magnitude squared of theoverlap integral |I_(mknl)|² would be obtained that is similar toEquation (17), but reduced by a factor of four.

[0078] Therefore, the LRHF g_(mk) is defined by the real value m andinteger parameter k, where real value m defines in the parameter α_(m)as: $\begin{matrix}{\alpha_{m} = \frac{2\pi \quad m}{\ln \left\lbrack {R_{2}/R_{1}} \right\rbrack}} & (18)\end{matrix}$

[0079] In a typical application the LRHF g_(mk) is evaluated over adiscrete image with a finite size, and where the pixel positions (x,y)only contain discrete integer values. To avoid aliasing, constraints areimposed on the allowable values for the parameters k and α_(m).

[0080] The LRHF g_(mk) has a well defined local frequency q(x,y), whichis defined as the modulus of the gradient of the phase Ψ_(mk) of theLRHF g_(mk) (γ), so $\begin{matrix}{{2\pi \quad {q\left( {x,y} \right)}} = \sqrt{\left( \frac{\partial\Psi_{mk}}{\partial x} \right)^{2} + \left( \frac{\partial\Psi_{mk}}{\partial y} \right)^{2}}} & (19)\end{matrix}$

[0081] where

g _(mk) =|g _(mk)|exp(iΨ _(mk))  (20)

[0082] Hence, from Equation (13), the phase Ψ_(mk) is

Ψ_(mk)=α_(m) lnγ+kθ  (22)

[0083] $\begin{matrix}{\frac{\partial\Psi_{mk}}{\partial x} = {{{\frac{\alpha_{m}}{r}\frac{r}{x}} + {k\frac{\theta}{x}}} = \frac{{x\alpha}_{m} - {ky}}{r^{2}}}} & (22) \\{\frac{\partial\Psi_{mk}}{\partial y} = {{{\frac{\alpha_{m}}{r}\frac{r}{x}} + {k\frac{\theta}{x}}} = \frac{{y\alpha}_{m} + {ky}}{r^{2}}}} & (23)\end{matrix}$

[0084] Substituting Equations (22) and (23) into Equation (19), localfrequency q(x,y) is: $\begin{matrix}{{q\left( {x,y} \right)} = \frac{\sqrt{\alpha_{m}^{2} + k^{2}}}{2\pi \quad r}} & (24)\end{matrix}$

[0085] In other words, the radial and tangential frequencies are squareadditives. In fact the full 2D frequency is just the vector sum of theradial and tangential frequency vectors. It is also noted that theorientation of the local frequency q(x,y) is always fixed relative tothe polar angle θ: $\begin{matrix}{{{\tan \left\lbrack {\frac{\partial\Psi_{mk}}{\partial y}/\frac{\partial\Psi_{mk}}{\partial x}} \right\rbrack} = {{\tan \left\lbrack \frac{{y\alpha}_{m} + {kx}}{{x\alpha}_{m} - {ky}} \right\rbrack} = {\tan \left\lbrack {\chi + \theta} \right\rbrack}}}{where}} & (25) \\{{{\tan \lbrack\chi\rbrack} = \frac{k}{\alpha_{m}}},{{\tan \lbrack\theta\rbrack} = \frac{y}{x}}} & (26)\end{matrix}$

[0086] This property means that spirals in the LRHF g_(mk) areequi-angular.

[0087] The minimum frequency q_(min) for an annular LRHF g_(mk) occursat the maximum radius R₂ and the maximum frequency q_(max) at theminimum radius R₁ defined respectively by: $\begin{matrix}{{Q_{\max} = \frac{\sqrt{\alpha_{m}^{2} + k^{2}}}{2\pi \quad R_{1}}},{q_{\min} = \frac{\sqrt{\alpha_{m}^{2} + k^{2}}}{2\pi \quad R_{2}}}} & (27)\end{matrix}$

[0088] The maximum frequency q_(max) is kept below the Nyquist frequencyof the discrete image. FIGS. 3A and 3B show the real and imaginary partsrespectively of a typical LRHF g_(mk) with parameters k=50 and α_(m)≅50.

[0089] The foregoing described the basic properties of LRHFs. However,the property of most interest in this implementation is theircorrelation property. Correlation at the origin has been dealt with inthe overlap integral I_(mkln).

[0090] In the more general case of cross-correlation andauto-correlation, a 2D-correlation function is obtained. An efficientmethod of correlating two large image functions is via the Fast FourierTransform (FFT).

[0091] It is convenient to work with continuous Fourier Transformsinitially, although much of the mathematics transfers directly to thediscrete case with discrete Fourier transforms, with the exception ofinfinite frequency parts. Consider first the case of purely radialfunctions with complex exponent c, having the form of Equation (8), andits transform: $\begin{matrix}\left. r^{- c}\Leftrightarrow{q^{c - 2}2^{1 - c}\frac{\Gamma \left( {1 - {c/2}} \right)}{\Gamma \left( {c/2} \right)}} \right. & (28)\end{matrix}$

[0092] Here Γ() is the generalised factorial (gamma) function. Usingpartial derivatives it can be shown that LRHFs g_(mk) having the form ofEquation (13), have the following transform pair:

γ^(ρ)γ^(iα,) e^(ik0)

μ_(mkp)q^(−p−2)q^(−iαm)e^(lkφ)  (29)

[0093] The parameter μ is a complex constant related to the gammafunction Γ( ). It is noted that no coordinate scaling is necessary toestimate the form of the Fourier transform. In fact the Fourier phase φis essentially the same as the spatial phase θ, except for a signreversal in the radial component. This can be seen from the following:

arg[γ ^(p)γ^(iα)e^(inθ) ]=αln[γ]+nθ  (30)

arg[μ _(mkp) q ^(−p−2) q ^(−iαm) e ^(lkθ) ]=const−α _(m) ln[q]+kθ  (31)

[0094] One of the principle applications of correlation in imageprocessing is in the area of template matching. Correlation is thereforeused to detect the presence of a pattern, such as a LRHF g_(mk), in animage ƒ, where the image ƒ(x,y)=p(x,y)+g_(nl)(x,y). Correlation betweenpattern g_(mk) and image ƒ produces a 2 dimensional image with maximumvalues at positions where the image ƒ best matches the pattern g_(mk).The Fourier correlation theorem provides:

h(x,y)=ƒ(x,y){circle over (x)}g(x, y)

F^(m)(u,v)G(u,v)=H(u, v)  (32)

[0095] Thus, correlation can be implemented by Fourier transforming theimage ƒ and the pattern g to obtain Fourier transformed functions F andG, complex conjugating one of the Fourier transformed functions, say F,and then multiplying these two functions F^(m) and G, beforetransforming back.

[0096] It is also noted that:

h(x,y)=[p(x,y)+g _(ml)(x,y)]{circle over (x)}g _(mk)(x, y)

=[p(x, y){circle over (x)}g _(mk)(x, y)]+[g _(mk)(x,y){circle over (x)}g_(mk)(x, y)]  (33)

[0097] Hence, the effectiveness of the embedding and detection ofpattern g_(mk) in typical images depends on the cross-correlation of theoriginal image p with the chosen pattern g_(mk) being of low magnitudeand widely dispersed. This is difficult to estimate however, generally,the cross-correlation part is very small compared to theauto-correlation part. The heuristic argument for this is that LRHFs donot resemble features in typical images p. The LRHFs proposed have bothwide spatial support and wide spectral support.

[0098] Consider the correlation between two LRHFs g_(mk)(γ) andg_(nl)(γ), being the second term in Equation (33). The Fouriertransforms of the LRHFs g_(mk)(γ) and g_(nl)(γ) are of the form:

g _(mk)(r)=r^(ρ)r^(iαm) e ^(lkθ)

μ_(mkp) q ^(−p−2) q ^(−iαm) e ^(lkφ)  (34)

g _(nl)(r)=r^(ρ)r^(iαm) e ^(ilθ)

μ_(nlp) q ^(−p−2) q ^(−iαm) e ^(ilφ)  (35)

[0099] The product of the complex conjugate of the transform of LRHFg_(mk)(γ) and the transform of g_(nl)(γ), provides:

H _(mknl)(u, v)=μ_(mkp) q ^(−p−2) q ^(+iαm) e ^(−ikφ)μ_(nlp) q ^(−p−2) q^(iαn) e ^(ilφ)=μ_(mkp)μ_(nlp) q ^(−2p−4) q ^(l(am−an)) e^(1(l−k)φ)  (36)

[0100] The phases partly cancel when the two chosen LRHFs g_(mk)(γ) andg_(nl)(γ) are similar. Only when the functions are identical do thephases entirely cancel out. Phase cancellation is the classic conditionfor maximum correlation, although a purely linear phase component canexist and only indicates a shift in the two original functions.

[0101] In the case where the two LRHFs g_(mk)(γ) and g_(nl)(γ) areidentical, Equation (36) reduces to:

H _(mknik)(u, v)=(μ_(mkp))² q ^(−2ρ−4)   (37)

[0102] In such a case the correlation peak will be of the form$\begin{matrix}{{{{\left( g_{mk} \right) \otimes g_{nl}}}} \approx \frac{{g_{mk} \otimes g_{nl}}}{2}} & (39)\end{matrix}$

[0103] The above equations are ideals, and the correlation peaks will befinite and discrete approximations to the ideal in practice.

[0104] However, the pattern g_(nl)(x,y) is typically limited to realvalues only when embedding in the discrete imageƒ(x,y)=p(x,y)+g_(nl)(x,y). The discrete image ƒ(x,y) is typicallyfurther limited by only 8 bits of data per pixel, thus greyscale levels0-255. As noted earlier, all the preceding analysis extends easily tothe case where a real pattern R(g_(mk)) is embedded in an image p(x,y)and detected with a complex pattern g_(nl). The main difference is a 2times increase in the noise compared to the full complex correlation,or: $\begin{matrix}\left. \begin{matrix}{{{h_{mkmk}\left( {x,y} \right)} \propto r^{2{({p + 1})}}},} & {p \neq {- 1}} \\{{{h_{mkmk}\left( {x,y} \right)} \propto {\delta \left( {x,y} \right)}},} & {p = {- 1}}\end{matrix} \right\} & (38)\end{matrix}$

[0105] Another difference is that the correlation of a pattern g_(nl)with the real part of that pattern g_(nl) is no longer a real power ofγ. Some oscillating structure will “leak” through, both radial andtangential.

[0106] The underlying mathematical method of LHRF correlation isinvariant to any scale and rotation variation such that:

g(γ,θ){circle over (x)}N{g(αγ, θ+φ)}=[g(γ,θ){circle over(x)}N{c.g(γ,θ)}]  (40)

[0107] wherein N defines a real or imaginary component, γ is adisplacement distance, θ and φ are angles, α is a positive real number,and c is a complex number not dependent on said displacement distance γnor said angle θ.

[0108] In a similar manner functions can be defined so that thecorrelation is invariant to any scale variation such that:

g(γ, θ){circle over (x)}N{g(α.γ,θ)}=[g(γ,θ){circle over(x)}N{c.g(γ,θ)}]  (41)

[0109] wherein c is a complex number not dependent on said displacementdistance γ nor said angle θ.

[0110] Further functions can be defined so that the correlation isinvariant to any rotation variation such that:

g(γ,θ){circle over (x)}N{g(γ,θ+φ)}=[g(γ,θ){circle over(x)}N{c.g(γ,θ)}]  (42)

[0111] wherein c is a complex number not dependent on said displacementdistance γ nor said angle θ, and the function g (γ,θ) does notnecessarily have circular symmetry. In the case of circular asymnmetrythe relation g(γ,θ)≢g(γ) holds. Many common functions and patterns withsimple N-fold rotation symmetry are excluded from the above definitionbecause they do not generally satisfy Equation (42) for all values of φ;only for special values of the rotation angle φ=2π/N. An example of sucha pattern is composed of three circles centered on the vertices of anequilateral triangle. Such a pattern has tri-fold rotational symmetryand repeats for rotation angles of φ=2π/3, and for all other anglesEquation (42) is violated.

[0112] As noted before, the maximum frequency q_(max) is kept below theNyquist frequency of the discrete image. The maximum frequency q_(max)is as defined in Equation (27), and determines the size of the ‘hole’ inthe centre of the pattern. Similarly the size of the image introduces amaximum pattern size. In the simplest case, the pattern is restricted toan annular region defined by radii R₁ and R₂.

[0113] In addition to the conventional correlation process outlinedabove, and in particular Equations (36), (37) and (38), enhanced formsof correlation may also be usefully employed for the detection ofembedded patterns.

[0114] One form of enhanced correlation is to boost the high frequencycomponents of the conventional correlation. This has the effect ofchanging the real exponent p in Equations (37) and (38) resulting in acorrelation peak which resembles the delta function in the second partof Equation (38).

[0115] Another form of enhanced correlation is known as “phase-only”correlation. Phase only correlation is implemented by taking the Fouriercorrelation magnitude, expressed in Equation (37) for example, andsetting it to unity. This ensures that only the phase terms contributeto the overall correlation peak. Again, the peak shape tends to resemblea delta function.

[0116] A variety of enhanced correlation processes, which consist ofintermediates between frequency-boosted correlation and phase-onlycorrelation, are also possible and applicable to the correlationdetection.

[0117] Roughly speaking, the ratio of the two radii R₁ and R₂ in theannulus determine the extremes of the possible scale variations beforecorrelations fail completely. Hence, the minimum scaling factor is R₁/R₂and the maximum is R₂/R₁. Preferably, the limits are set at 50% overlaparea between an embedded pattern g_(km) and a detection pattern g_(ln),in which case the two scaling ratios are: $\begin{matrix}{{\sqrt{\frac{1}{2}}\sqrt{1 + \frac{1}{2\lambda^{2}}}\quad {and}\quad \sqrt{\frac{1}{2}}\sqrt{1 + \frac{\lambda^{2}}{2}}\quad {where}\quad \lambda} = \frac{R_{1}}{R_{2}}} & (43)\end{matrix}$

[0118] The range factor in this case is $\begin{matrix}{\lambda \sqrt{\frac{2 + \lambda^{2}}{1 + {2\lambda^{2}}}}} & (44)\end{matrix}$

[0119] In a typical case, for example, where λ=4, then the ratios are0.72 and 2.12.

[0120] The range of scale variation may be extended by performing thecorrelation upon a number of differently scaled versions of thewatermarked image. This allows the overlap area to be improved in atleast one of the correlations. So, for example a sequence of imagesrescaled by progressive factors of 2 would guarantee one of the imagesto fit the 50% overlap criterion (for λ≧4), and hence give a strongcorrelation peak.

[0121] The foregoing described the properties of LRHFs. FIG. 4 shows aschematic diagram of a process 450 of watermarking an image 400 ordocument with a pattern 410, such as the real part of a LRHF g_(mk)shown in FIG. 3A. The pattern 410, which may be called a watermark, issimply added to the image 400 to form a watermarked image 420. If theimage 400 is in colour, then the pattern 410 is added to the luminancepart of a colour image 400. This allows the watermark to survive whenthe watermarked image is converted from colour to a greyscalerepresentation.

[0122] Preferably, the pattern 410 component in the watermarked image420 is invisible or imperceptible to the human visual system undernormal viewing conditions. This is done by multiplying the pattern 410with a constant embedded factor 430, thereby adding a low intensity copyof the pattern 410 to the image 400.

[0123] A problem with embedding the low intensity copy of the pattern410 at a sufficiently low level for it to be imperceptible to the humanvisual system, is that the signal levels of the low intensity copy ofpattern 410 may be of a magnitude comparable to the quantisation stepsize used in a digital system. Consequently a simple quantisation stepmay lose the watermark information in a significant number of the signalsamples. However, by using methods such as error diffusion, the loss ofthe watermark by quantisation in one sample is compensated by theincreased likelihood of the watermark being represented by a nearbysample.

[0124] A collection of patterns may also be added to the image 400. FIG.5 shows the sum of 6 shifted LRHFs, similar in form as those shown inFIG. 3A. Bcfore patterns are added to images for watermarking, a scaleis applied to their intensity, or the intensity of their sum in the caseof a collection of patterns, so that their intensity is approximately ofthe range −5 to +5 (for example) to avoid wide intensity variation. Itis noted that the intensities of the image shown in FIG. 5 has beenamplified to the range 0-255 to more clearly show the patterns.

[0125]FIG. 6 shows the watermarked image formed by adding the watermarkrepresented in FIG. 5 to a test image, in this case Lena. The watermarkis perceptible in regions having low intensity variation, such as region501.

[0126] In a preferred implementation, an adaptive scheme is used toreduce the level of the watermark in regions having low intensityvariation and increase the level of the watermark in regions of highintensity variance. The watermark is a real function with the followinggeneral form:

ĝ _(k,m,n)(x, y)=R{g(γ,θ)}=R{w _(n)(γ,θ)γ^(ρ)γ^(iαm) e ^(ikθ)}  (45)

[0127] The window function w_(n)(γ,θ) is a slowly varying functionrelatively to the pattern function γ^(ρ)γ^(iαm)e^(ikθ). Firstly, thewindow function w_(n)(γ,θ) is used to remove or de-emphasise the highfrequency central region of the pattern function γ^(ρ)γ^(iαm)e^(ikθ).Furthermore, the window function w_(n)(γ,θ) is also used to reduce thepattern intensity in regions of an image to which it is applied, wherethe pattern would otherwise be highly visible, such as “flat” skyregions. The de-emphasis window function w_(n)(γ,θ) may be calculated byestimating the perceptual masking in various regions of the image. Anexample measure of perceptual masking is local gradient magnitude of theluminance in the inage. Others include second partial derivatives of theluminance; local estimates of the “energy” or frequency content, localvariance, and more sophisticated estimates of human visual systemmasking.

[0128]FIG. 7A shows a schematic diagram of an alternative process 750 ofwatermarking an image 700. A perceptual mask 720 is formed from theimage 700. The pattern 710 with parameters k and m (or a combination ofpatterns) is then de-emphasised with the perceptual mask 720 bymultiplying the pixel values of the perceptual mask 720 withcorresponding pixel values of the pattern 710. The resulting pattern isof the form of Equation (45). This de-emphasised pattern is added to theimage 700 to for a watermarked image 730.

[0129] Preferably, the pattern 710 component in the watermarked image730 is invisible or imperceptible to the human visual system undernormal viewing conditions. This is done by multiplying the pattern 710with a constant embedded factor 740, thereby adding a low intensity copyof the pattern 710 to the image 700.

[0130]FIG. 7B shows the watermarked image formed by adding the watermarkrepresented in FIG. 5 to the test image, using the process 750 shown inFIG. 7A. The watermark that was perceptible in region 501 of FIG. 6 isno longer perceptible in a corresponding region 502.

[0131] The window function w_(n)(γ,θ) can also contain otherinformation, for example a constant phase (ie complex) factor. Such aphase factor causes a constant phase offset to the pattern functionγ^(ρ)γ^(iαm)e^(ikθ). In one implementation, this phase factor is maderandom, making every watermark unique, even when the same parametersα_(m) and k are used. Such a watermark would be even harder to detect.

[0132] Again, with colour images, the de-emphasised pattern ĝ_(k,m,n)(x,y) may be added to the luminance part of the signal. Alternatively, thede-emphasised pattern ĝ_(k,m,n)(x, y) may be added to the R, G, B, H, V,S, u, v etc channels of the colour image, or any combination thereof.

[0133] The watermark that is embedded into an image generally consistsof a summation of separate basis patterns ĝ with varying location,windows, and tuning parameters:

Σ_(M=1) ^(N) w′ _(n)(x−x _(n) , y−y _(n))·ĝ _(k(n),m(n),n)(x−x _(n) ,y−y _(n))  (46)

[0134] where window function w′_(n) removes or de-emphasises the highfrequency central region of each of the separate basis patterns ĝ.

[0135] The window function w(x,y) for applying perceptual de-emphasismay be applied after the summation process, to form a watermark asfollows:

w(x, y)Σ_(M=1) ^(N) w′ _(n)(x−x _(n) , y−y _(n))·ĝ_(k(n),m(n),n)(x−x_(n) , y−y _(n))  (47)

[0136] The watermark encodes information in the centre location(x_(n),y_(n)) strength, relative phase, and parameters k(n) and α_(m)(n)of each of the N basis patterns ĝ. In practice the centre location(x_(n),y_(n)) strength is not a robust carrier of information, as it canbe easily attenuated, even accidentally, by any processing of thewatermarked image.

[0137]FIG. 8 shows a schematic diagram of a process 800 of detecting awatermark in a watermarked image 810. The watermarked image 810 issimply correlated with a complex pattern 820 having parameters k andα_(m), such as that shown in FIGS. 3A and 3B, to form a result image830. Referring to Equation (33), if the complex pattern 820 is presentin the watermarked image 810, in particular the real part of a LRHFhaving parameters k and α_(m), then the result image 830 will havecorrelation magnitude peak(s) at centre location(s) where that pattern820 was embedded into the image. The use of different parameters, say land α_(n), in the pattern 820 will result in no correlation magnitudepeaks in the result image 830.

[0138] With more than one basis pattern ĝ used in the watermark, theprocess 800 of detection may be repeated for each of the basis patternsĝ.

[0139] The process 800 may also be used with watermarked images 810where process 750 shown in FIG. 7A was used to embed the watermark 710into the image 700, using de-emphasis of the watermark.

[0140]FIG. 9 shows a schematic diagram of an alternative process 900 ofdetecting a watermark in a watermarked image 910. A perceptual mask 920is formed from the watermarked image 910. The watermarked image 910 isthen emphasised with the perceptual mask 920 by dividing the pixelvalues of the watermarked image 910 by pixel values of correspondingpixel values of the perceptual mask 920. This emphasised image 930 iscorrelated with the complex pattern 940 to for a result image 950.

[0141]FIG. 10A shows the magnitude image of the correlation of thecorrect LRHF g_(mk)(γ) with the watermarked image of FIG. 6 usingprocess 800. FIG. 10B shows the detail of the peak structure of one ofthe magnitude peaks of FIG. 10A. FIG. 11A shows the magnitude image ofthe correlation of the correct LRHF g_(mk)(γ) with the watermarked imageof FIG. 7B using process 900, whereas FIG. 11B shows the detail of thepeak structure of one of the magnitude peaks of FIG. 11A. Note that themagnitude peaks shown in FIGS. 10B and 11B are very sharp and clear,whereas the background correlation is small. An improvement in thesharpness of the magnitude peaks is also visible in FIG. 11B. Thus,whereas the watermark process 750 using de-emphasis makes the patternless perceptible, the watermark detection process 900 using emphasisimproves detection by resulting in sharper magnitude peaks.

[0142] The magnitude peaks can only be detected by correlation with theknown LRHF(s) used for embedding, or by an exhaustive search ofcorrelation magnitude peaks by using the full range of parameters k andα_(m). The exhaustive search can be expected to be many orders ofmagnitude slower than detection using the correct parameters k andα_(m), making the method difficult to attack.

[0143]FIG. 12 shows the watermarked image of FIG. 7B rotated by 20degrees and increased in size by 20%. The image has also been croppedand a gamma correction power of 0.8 has been applied. These operationswere performed on the 8-bit image data using linear interpolation.

[0144] Performing the watermark detection process 900 shown in FIG. 9,using the correct detection LRHF g_(mk)(γ), the result shown in FIG. 13is obtained. FIG. 14 shows the detail of the peak structure of one ofthe magnitude peaks of FIG. 13. There is some degradation of the peakstructure compared to the magnitude peaks of FIG. 11B, but thecorrelation magnitude peaks are still well above the background noiselevel.

[0145] For an image containing a single magnitude peak, detection isrelatively straightforward, in that the pixel containing the maximummodulus value is selected, and its coordinates define the centre of theembedded pattern.

[0146] For images containing multiple peaks to be detected, a slightlymore complex approach is used. If a detection image contains s peaks,those s peaks may be detected as follows:

[0147] Find the pixel with maximum modulus among pixels inconsideration. This pixel p_(i) is one of the s pixels;

[0148] Exclude all pixels in a disk of some radius q around pixel p_(i)from consideration; and

[0149] Repeat s times in total.

[0150] The radius q is chosen depending upon the application. Whenalignment peaks are very well spaced, a large value for q, say 20pixels, may be used. Peaks used to encode information may be much closertogether, and a smaller value for q should be used.

[0151] The proposed processes of watermarking and detection ofwatermarks are inherently robust to most image distortions. Theseinclude:

[0152] Scale change from about 50% to +200%;

[0153] Any rotation;

[0154] JPEG compression down to about a 10:1 compression;

[0155] Gamma correction; and

[0156] Low pass filtering.

[0157] In addition to the above, the method is more difficult to defeatthan known methods where the watermarks can be detected by analysing theFourier magnitudes of an image. Detection of LRHF g_(mk)(γ) basedwatermarks requires many correlations, typically more than 1000, if theparameters α_(m) and k of the LRHF g_(mk)(γ) are unknown.

[0158] In the forgoing the LRHF is restricted to an annular regiondefined by radii R_(i) and R₂. However, square or other shapes may alsobe used to restrict the patterns. FIG. 16A shows the real part of anexample a LRHF restricted within a sub-region having an trapezoidalshape. Even though the sub-region does not in itself have any rotationalsymmetry properties, nor is it strictly orthogonal, it is neverthelessdetected effectively at any rotation angle by correlation with a fullcircular complex LRHF. Accordingly, either of process 800 or 900 shownin FIGS. 8 and 9 respectively may be used to detect such a patternhaving an arbitrary shape. The scaling and cropping invariant propertiesare similarly maintained.

[0159]FIG. 16B shows the intensity of a correlation magnitude peak as aresult of correlating a square LRHF with a circular complex LRHF. Thismay be compared with the intensity of the correlation magnitude peak asa result of correlating the arbitrarily shaped LRHF shown in FIG. 16Awith the circular complex LRHF, which is shown in FIG. 16C. It can beseen that a distinct peak is still formed which may be detected in theusual manner. The magnitude peak shown in FIG. 16C tends to beelliptical rather than circular in the specific example, with theintensity of the sidelobes being about 30% of that of peak value.

[0160] There are many applications in machine and computer vision thatrequire registration and alignment of objects. One such an applicationis when a message is embedded in an image by defining a set of centrelocations (x_(n),y_(n)) for basis patterns ĝ and adding basis patterns ĝat selected ones of those centre locations (x_(n),y_(n)).

[0161] Watermarks based on LRHFs are particularly suited for embeddingalignment marks in images to allow reliable registration and alignmentof an image of, or applied to the object. Such alignment marks couldtake many forms. In a particular implementation, three basis patterns ĝare added to the image, with the basis patterns ĝ having centrelocations (x_(n),y_(n)) corresponding with the positions of threecorners of a square of known size forming an ‘L’-shape. The basispatterns ĝ may be embedded visibly or invisibly using process 450 or 750set out above.

[0162] The detection of the possibly transformed centre locations(x_(n),y_(n))′ of the alignment marks is performed by using method 800or 900, shown in FIGS. 8 and 9 respectively. Once the alignment marks inthe form of magnitude peaks in the resulting magnitude image aredetected, the translation may be estimated as follows:

[0163] A rotation angle may be estimated using the vector between thetwo detected centre locations (x_(n),y_(n))′ or peaks which are furthestapart. Similarly, a total scaling factor may be estimated using thedistance between these two peaks. A shear factor may be estimated bymeasuring the angle between the three peaks. A change in aspect ratiomay be estimated by measuring the difference in the length of thehorizontal side and the vertical side of the “L” shape formed by thethree peaks. The middle point of the ‘L’ shape may be used to define thecoordinate system origin of the alignment marks.

[0164] The four parameters (angle, scaling, shear and aspect ratio)completely define a linear transformation. Reflections and non-lineartransformations such as warping or removal of image columns or rows cannot be detected and therefore can not be inverted. The lineartransformation may be inverted to restore the watermarked image to itsoriginal size and orientation.

[0165] Scaling and rotation may be performed by a variety of resamplingalgorithms. Typically a high quality resampling using bi-cubicinterpolation, Fourier interpolation, or even a non-linear resamplingscheme may be used.

[0166] Once the watermarked image is returned to its nominal settings,an alternative watermarking or steganographic method may be utilised toextract further information from the image.

[0167] In another implementation, the registration patterns are used inconjuction with any other watermarking technique. The registration isperformed before reading the embedded watermark.

[0168] Registration may include focusing because the correlationmagnitude peaks provide a nice smooth variation in magnitude withrespect to changes in the focus of imaging systems. Focus can beestimated by correlation peak width. An advantage of a width basedmeasure of focus is that it is normalised and does not depend upon theabsolute peak level.

[0169] Registration may further include aspect ratio correction andshearing to some extent, due to the strength of the correlationmagnitude peaks.

[0170] The above patterns used as the watermark were allradial-tangential functions having the form of Equation (45). However,patterns that only vary in one dimension may also be used, such aspatterns of the following form:

g _(m)(x, y)=R{w(x, y)|x| ^(lαm)}  (48)

[0171] This pattern only has variation in a x direction. Any directioncould be chosen in practice. Process 450 or 750, shown in FIGS. 4 and 7respectively, may be used to embed the pattern into an image.

[0172] The one dimensional pattern may be detected using process 800 or900, shown in FIGS. 8 and 9 respectively, to detect the centre lineposition of a pattern, if the correct parameter α_(m) is known. Inparticular, a two-dimensional complex pattern having the form ofEquation (13) is used as the pattern 820 in process 800, with thetwo-dimensional complex pattern having the same parameter α_(m), butzero spiral parameter k. The detection is unaffected by shear oranamorphic magnifications.

[0173] It is also possible to construct scale invariant patterns from aseparable product of one dimensional patterns, thus having the form:

s _(l,m)(x, y)=w(x, y)|x′| ^(lαi+ρs) |y′| ^(lαm+ρs)   (49)

[0174] However, such patterns are not rotation invariant. It is notedthat the separable directions (x′, y′) do not need to be orthogonal. Asequence of the above patterns may be summed to form the overallwatermark. Radial harmonic patterns of the form of Equation (45) mayalso be added. In one implementation, the radial harmonic pattern(s) isadded for registration, allowing the watermarked image to be rotatedback to its original orientation, before the pattern is detected byusing one of the detection processes 800 or 900.

[0175] As stated above, the watermark encodes information in the centrelocation (x_(n),y_(n)) strength, phase, and parameters k(n) and α_(m)(n)of each of the N basis patterns ĝ. For example, the location(x_(n),y_(n)) of each peak could store several bits of data. Moresophisticated methods may also be used such as described below.Detection of the stored data requires that the peak and its position beidentified reliably. This process may entail some error correcting ordata redundancy scheme.

[0176] Using the peak localisation property, several independentwatermarking basis patterns ĝ, with each basis pattern ĝ centred on apixel in a 64×64 square grid in the image which is used forwatermarking. To allow accurate extraction, each grid position ispreferably separated by 7 pixels, thus the template grid pattern coversa region of 448×448 pixels in the candidate image, which is small enoughto embed in all but the smallest images.

[0177] Because the detection error is usually small and typically within1-2 pixels, a scaling factor of 50% would result in a grid spacing of3.5 pixels, which is still reliably detectable. Any scaling to smallerdimensions could result in errors during message decoding. Scaling toincreased image size could tend to enhance the reliability of detection.

[0178] This technique uses three points on a regular grid to provideinformation on the pattern orientation and scaling, a point to encodeimage length, and subsequent points to encode bits of information.

[0179] Once the embedding grid has been established, each row and columnposition of the marks in the original grid may be derived from thedetected position of each basis embedded in the watermarked image.

[0180] The first three points define the corners of the embedding grid.A different basis pattern ĝ defines each point, thus they may bedetected in order and their relative positions used to establish theorientation and scaling of the grid in the watermarked image, andsufficiently small shear or anamorphic scaling changes.

[0181] From the three corners of the grid, a linear transformation maybe derived from the coordinates of the watermarked image to that of theoriginal 64 point by 64 point grid.

[0182] The fourth point in the sequence of detected bases is used toencode the length of the encoded message in bits. By assigning numbersfrom 0 to 4095 to each grid position, the fourth point may indicate amessage of any length from 0 to 4095 bits.

[0183] Subsequent points encode the bits of the message by concatenatingthe bits representing the row and column address of each point. In a 64point by 64 point grid, each row or column address codes exactly 64 (2⁶)separate values. Hence, each point on the 64×64 grid encodes up to 12bits.

[0184] Modifications to this simple technique provide encoding schemeswith slightly different properties.

[0185] By embedding patterns on a 64 point by 64 point grid with only asingle basis pattern ĝ and B points, messages of └log₂(⁴⁰⁹⁶C_((B−3)))┘bits using three alignment points may be stored, where C is the binomialcoefficient and ␣ is the floor operator. There are two advantages ofthis technique. Firstly, only a single correlation need be performedduring detection, thus providing a faster detection method. Secondly,any image transformation will affect the relative phase of all detectedpoints similarly. This provides an opportunity to encode at least oneextra bit of information per basis, by comparing the complex phase ofeach detected peak with that of the first.

[0186] Encryption may be performed on the bitstream to hide informationfrom persons not holding the appropriate keys.

[0187] Checksums may be added to the bitstream to provide verificationof the detected watermark, and also as an aid in locatinginformation-containing watermark patterns.

[0188] Error-correcting codes may be added to the bitstream to increasethe robustness of the encoded bitstream, albeit with the requirement ofembedding more basis patterns ĝ in the original watermark, perhapsmaking the mark more visible.

[0189] To make the embedded pattern harder to discover with maliciousintent, multiple basis patterns ĝ may be added together at the sameposition and the sum of their detection magnitude peaks used duringdetection. In this case, each detection peak alone may be too small tomeasure, but the summation of the amplitude of all detection images willcombine to produce a very well-defined peak. Only by knowing a largefraction of the multiple bases can the detection peak and hence thebasis for watermarking, be found.

[0190] The process of embedding and detecting rotation and scaleinvariant bases has several properties, which provide the means to embeda substantial amount of information in an image watermark and recover itwith great reliability. These properties include:

[0191] The amplitude peaks recovered from a watermarked image areextremely sharp and well localized, typically within 1-2 pixels. Thustheir embedded position in the original image can be recovered with agreat degree of accuracy.

[0192] Each watermarking basis pattern ĝ is orthogonal to all otherbases having different parameters k and α_(m). Thus, if many differentbases patterns ĝ are used in the watermark, a peak for each basis may berecovered almost independently of all other bases patterns ĝ.

[0193] If a single basis pattern ĝ is used to embed a watermark, themagnitude peaks in the detected image will all be of identical complexphase. If multiple basis patterns ĝ are used which differ only incomplex phase, i.e. each basis pattern ĝ is multiplied by a differentcomplex constant of unit modulus, then the relative phase of alldetected magnitude peaks will be preserved. In the best case, a singledetected point may be used to determine the base phase, and the phase ofsubsequent magnitude peaks in the result image will retain theirrelative relationship to this base point.

[0194] The sharpness and amplitude of detection magnitude peaks is notsubstantially affected by any rotation or scaling transformationsapplied to the image, although the position of the magnitude peaksthemselves will be rotated and scaled with the watermarked image. Thus,any rotation or scaling can be detected and corrected for by using theposition of alignment points.

[0195] To a certain extent, shearing or anamorphic (aspect ratio)changes may also be detected and taken into account, thus the method isapplicable to arbitrary linear transformations as long as the shear,scaling or anamorphic component is small enough.

[0196] By using iterative searching, any linear transformation to thecoordinate system of a watermarked image that did not ruin its contentcould be detected and corrected for.

[0197] In addition to the aforementioned uses for embedded patterns,there are numerous other applications, some of which will now mentioned.

[0198] The use of a watermark allows a code to be embedded into animage. Such a code will remain with the image even if the header andother metadata of the image file are removed. This allows the code toremain strongly attached to the actual image itself. The code may beusefully employed to define the address or location of the originalmetadata related to the image. The metadata may contain owneridentification, camera settings, geographical location, details of thesubjects in the image, or any number of pieces of other information.Image metadata may be stored on the same device as the image, or on aserver connected by a network, or even a server owned by a third partyon the Internet.

[0199] A watermark can also embed a copyright owner's information intoan image. The copyright information will be difficult to detect orremove by anyone who does not have knowledge of the parameters used todefine the embedded patterns. Without the embedded pattern parameters itis necessary to search a large number of possible configurations beforecorrelation peaks may be detected. The difficulty in searching may besufficient to dissuade attacks upon this copyright making method.

[0200] The processes 450, 750, 800 and 900 can be implemented on asystem 200 shown in FIG. 15. In particular, one or more of the processes450, 750, 800 and 900 may be implemented as software executing withinthe system 200, where the processes 450, 750, 800 and 900 are effectedby instructions in the software that are carried out by the system 200.The software may be stored in a computer readable medium, including thestorage devices described below, for example. The software is loadedinto the system 200 from the computer readable medium, and then executedby the system 200. A computer readable medium having such software orcomputer program recorded on it is a computer program product. The useof the computer program product in the system 200 preferably effects anadvantageous apparatus for watermarking, watermark detection orregistration.

[0201] The pattern embedding and detecting processes 450, 750, 800 and900 may be included as a plug-in module for commercially availablesoftware packages. In particular, packages which are used for themanipulation and editing of digital image files would benefit by theaddition of the pattern embedding and detection software.

[0202] The embedding and/or the detection of the watermarks may beoperated as a service by a third party. The images may be conveyed by adigital network for embedding and then returned to the owner with thehidden mark. Similarly an image thought to contain a mark may besubmitted to the third party operator for detection of marks withspecified parameters.

[0203] Libraries of digital images could incorporate embedded patternsto maintain connections with image metadata and also to maintain imagecopyright information.

[0204] Digital cameras, whether still or video would benefit from theinclusion of pattern embedding software and/or software to allowembedding of information immediately following image acquisition. Theadvantage in such a system is that unmarked images would be difficult orimpossible to obtain.

[0205] The system 200 may, for example, be a general-purpose computer, adigital camera, a video camera, a scanner or a photocopier. The system200 comprises a computer module 201, output device(s) 215 and inputdevices such as controls 202 and digital capture device 203. The digitalcapture device 203 may be an image sensor, such a two-dimensional CCDarray. The computer module 201 typically includes at least one processorunit 205, a memory unit 206, for example formed from semiconductorrandom access memory (RAM) and read only memory (ROM), input/output(I/O) interface(s) and a storage device 209. The components 205 to 213of the computer module 201, typically communicate via an interconnectedbus 204 and in a manner which results in a conventional mode ofoperation of the computer system 200 known to those in the relevant art

[0206] In the case where the system 200 is a general-purpose computer,the output device 215 includes a display device. A printer may also beprovided. The controls 202 include a keyboard and a mouse. The storagedevice 209 typically includes a hard disk drive, a floppy disk drive anda CD-ROM drive. Typically, the application program is resident on thestorage device 209, and read and controlled in its execution by theprocessor 205. Intermediate storage of the program may be accomplishedusing the semiconductor memory 206, possibly in concert with the storagedevice 209. In some instances, the application program may be suppliedto the user encoded on a CD-ROM or floppy disk and read via a CD-ROMdrive or floppy disk drive 211, or alternatively may be read by the userfrom a network (not illustrated). Still further, the software can alsobe loaded into the computer system 200 from other computer readablemedium including magnetic tape, a ROM or integrated circuit, amagneto-optical disk, a radio or infra-red transmission channel betweenthe computer module 201 and another device, a computer readable cardsuch as a PCMCIA card, and the Internet and Intranets including e-mailtransmissions and information recorded on websites and the like. Theforegoing is merely exemplary of relevant computer readable mediums.Other computer readable mediums may be practiced without departing fromthe scope and spirit of the invention.In the case where the system 200is a digital camera or video camera, the image(s) and/or the watermarkedimage(s) may be stored onto the storage device 209 or communicated toanother device (not illustrated).

[0207] One or more of the processes 450, 750, 800 and 900 mayalternatively be implemented in dedicated hardware such as one or moreintegrated circuits performing the functions or sub functions of thoseprocesses 450, 750, 800 and 900. Such dedicated hardware may includegraphic processors, digital signal processors, or one or moremicroprocessors and associated memories.

[0208] Thus, images may be obtained by the system 200 using the digitalcapture device(s) 202 or through the storage device 209. Watermarkedimages may be displayed, printed, stored or communicated to otherdevices. Similarly, watermarked images may be obtained by the system 200using the digital capture device(s) 202 or through the storage device209.

[0209] Before the watermarked image is displayed, printed or stored as agreyscale image on a medium which has a finite dynamic range andresolution, such as a bitmap file, liquid crystal display or alaser-printer output, the watermarked image is converted to a quantisedfacsimile or a halftone representation.

[0210] In another implementation, the digital capture device 203 is anaudio device, and the system 200 is used to embed watermarks of theform:

g _(m)(t)=|t| ^(lαm+ρ)  (50)

[0211] into audio streams, where t is a time in the audio stream.

[0212] Audio signals whether digital or (high quality) analogue may havevery low level patterns or signals added with very little differencesbeing perceptible. If the signal length is long enough, then a strongcorrelation peak is obtainable provided the pattern parameters areknown. In this way information (copyright or otherwise) may be embeddedin the audio signal. The embedding device, which may be software orhardware, may be located near the input of an audio capture device, suchas a microphone. Alternatively the embedding process may take place nearthe output device of an audio production system. In this case theembedded patterns would be optimised for the final output medium, suchas Compact Disc or Digital Audio Tape. The patterns would survive andstill be detectable after sophisticated watermark attacks such as pitchchanging and resampling because of the scale invariant property.

[0213] In yet another implementation, the correlation is performedoptically through the use of spatial light modulators.

[0214] The foregoing describes only some implementations, andmodifications and/or changes can be made thereto without departing fromthe scope and spirit of the invention, the implementation(s) beingillustrative and not restrictive.

We claim:
 1. A method of embedding a watermark into an image, saidmethod comprising the step of: maintaining at least one basis pattern;and adding said basis pattern(s) to said image, said basis pattern(s)being formed substantially from a basis function, wherein said basisfunction is defined such that said basis function when correlated with ascaled and rotated version of said basis function is substantially equalto the auto-correlation of said function within a complex multiplicativeconstant.
 2. A method as claimed in claim 1, wherein said at least onebasis pattern is a real function—substantially formed from said basisfunction.
 3. A method as claimed in claim 1, wherein said basis functionis a function g(γ,θ) defined such that: g(γ,θ){circle over(x)}g(α.γ,θ+φ)=c.[g(γ,θ){circle over (x)}g(γ,θ)] wherein γ is adisplacement distance, θ and φ are angles, α is a positive real number,and c is a complex number not dependent on said displacement distance γnor said angle θ.
 4. A method as claimed in claim 1, wherein said basisfunction is a function g(γ,θ) further defined such that: g(γ,θ){circleover (x)}N{g(α.γ,θ+φ)}=[g(γ,θ){circle over (x)}N{c.g(γ,θ)}] wherein Ndefines a real or imaginary component, γ is a displacement distance, θand φ are angles, α is a positive real number, and c is a complex numbernot dependent on said displacement distance γ nor said angle θ.
 5. Amethod as claimed in claim 1, wherein said basis function is of theform: g(γ,θ)=γ^(iαm+ρ)e^(lkθ), with k, p and α_(m) being parameters ofsaid basis function.
 6. A method as claimed in claim 1, wherein saidbasis pattern is of the form: g _(pinkn)(γ,θ)=R{w_(n)(γ,θ).γ^(iαm+ρ)e^(ikθ)} with k, p and α_(m) being parameters of saidbasis function, and w_(n)(γ,θ) is a window function, wherein a realcomponent of said basis pattern is added to said image.
 7. A method asclaimed in claim 6 wherein said window function w_(n)(γ,θ) removes orde-emphasises a central region of said basis function having frequenciesabove a predetermined frequency.
 8. A method as claimed in claim 6wherein said window function w_(n)(γ,θ) de-emphasises regions of saidbasis function corresponding with regions of said image having a lowsignal variation.
 9. A method as claimed in claim 6 wherein said windowfunction w_(n)(γ,θ) contains a constant phase factor.
 10. A method asclaimed in claim 5, wherein at least a first and a second basis patternsare added to said image, with said first and second basis patternsformed from a first and a second basis function respectively, and withat least one parameter k or α_(m) of said first basis function beingdifferent to that of said second basis function.
 11. A method as claimedin claim 5, wherein a plurality of basis patterns are added withdifferent offsets relative to a center of said image.
 12. A method asclaimed in claim 11 comprising the further initial step of encodinginformation into at least one of said parameters, said offset, anamplitude or a relative phase added to said basis pattern.
 13. A methodof embedding a watermark into an image, said method comprising the stepof: maintaining at least one basis pattern; and adding said basispattern(s) to said image, wherein said basis pattern(s) is formedsubstantially from a real component of a basis function, said basisfunction is of the form: s _(l,m)(x, y)=w(x, y)|x′| ^(lαl+ρx) |y′|^(lαm+ρy), wherein ρ_(x), ρ_(y), α_(l) and α_(m) are parameters of saidbasic function, w(γ,θ) is a window function, and x′ and y′ arepredetermined co-ordinates which are rotated relative to the Cartesianco-ordinates x and y.
 14. A method of embedding a watermark into animage, said method comprising the step of: maintaining at least onebasis pattern; and adding said basis pattern(s) to said image, saidbasis pattern(s) being formed substantially from a basis function,wherein said basis function is defined such that said basis functionwhen correlated with a scaled version of said basis function issubstantially equal to the auto-correlation of said function within acomplex multiplicative constant.
 15. A method as claimed in claim 14,wherein said basis pattern(s) is a real function—substantially formedfrom said basis function.
 16. A method as claimed in claim 14, whereinsaid basis function is a function g(γ,θ) defined such that:g(γ,θ){circle over (x)}g(α.γ,θ)=c.[g(γ,θ){circle over (x)}g(γ,θ)]wherein γ is a displacement distance, θ is an angle, α is a positivereal number, and c is a complex number not dependent on saiddisplacement distance γ nor said angle θ.
 17. A method as claimed inclaim 14, wherein said basis function is a function g(γ,θ) furtherdefined such that: g(γ,θ){circle over (x)}N{g(α.γ,θ)}=[g(γ,θ){circleover (x)}N{c.g(γ,θ)}] wherein N defines a real or imaginary component, γis a displacement distanice, θ is an angle, α is a positive real number,and c is a complex number not dependent on said displacement distance γnor said angle θ.
 18. A method of embedding a watermark into an image,said method comprising the step of: maintaining at least one basispattern; and adding said basis pattern(s) to said image, said basispattern(s) being formed substantially from a basis function, whereinsaid basis function is defined such that said basis function whencorrelated with a rotated version of said basis function issubstantially equal to the auto-correlation of said function within acomplex multiplicative constant.
 19. A method as claimed in claim 18,wherein said basis pattern(s) is a real function—substantially formedfrom said basis function.
 20. A method as claimed in claim 19, whereinsaid basis function is a function g(γ,θ) defined such that:g(γ,θ){circle over (x)}g(γ, θ+φ)=c.[g(γ,θ){circle over (x)}g(γ,θ)]wherein γ is a displacement distance, θ and φ are angles, α is apositive real number, and c is a complex number not dependent on saiddisplacement distance γ nor said angle θ.
 21. A method as claimed inclaim 19, wherein said basis function is a function g(γ,θ) furtherdefined such that: g(γ,θ){circle over (x)}N{g(γ,θ+φ)}=[g(γ,θ){circleover (x)}N{c.g(γ,θ)}] wherein N defines a real or imaginary component, γis a displacement distance, θ and φ are angles, and c is a complexnumber not dependent on said displacement distance γ nor said angle θ.22. A method of detecting a watermark from an image, said watermarkhaving a first basis pattern embedded, said method comprising the stepsof: maintaining a second basis pattern; and detecting said first basispattern in said image using said second basis pattern, said first andsecond basis patterns being formed substantially from a basis function,wherein said basis function is defined such that said basis functionwhen correlated with a scaled and rotated version of said basis functionis substantially equal to the auto-correlation of said function within acomplex multiplicative constant.
 23. A method as claimed in claim 22,wherein said at least one basis pattern is a real function—substantiallyformed from said basis function.
 24. A method as claimed in claim 22,wherein said basis function is a function g(γ,θ) defined such that:g(γ,θ){circle over (x)}g(α.γ,θ+φ)=c.[g(γ,θ){circle over (x)}g(γ,θ)]wherein γ is a displacement distance, θ and φ are angles, α is apositive real number, and c is a complex number not dependent on saiddisplacement distance γ nor said angle θ.
 25. A method as claimed inclaim 22, wherein said basis function is a function g(γ,θ) defined suchthat: g(γ,θ){circle over (x)}N{g(α.γ,θ+φ)}=[g(γ,θ){circle over(x)}N{c.g(γ,θ)}] wherein N defines a real or imaginary component, γ is adisplacement distance, θ and φ are angles, α is a positive real number,and c is a complex number not dependent on said displacement distance γnor said angle θ.
 26. A method as claimed in claim 22, wherein saidbasis function is of the form: g _(pmk)(γ,θ)=γ^(lαm+ρ)e^(ikθ), with k, ρand α_(m) being parameters of said basis function.
 27. A method asclaimed in claim 22, wherein said basis pattern is of the form: g_(pmkn)(γ,θ)=R{w _(n)(γ,θ)γ^(iαm+ρ)e^(ikθ)} with k, ρ and α_(m) beingparameters of said basis function, and w_(n)(γ,θ) is a window function,wherein a real component of said basis pattern is added to said image.28. A method as claimed in claim 22, wherein said detection stepcomprises the steps of: correlating said image with said second patternto form a correlation image; and locating at least one magnitude peak insaid correlation image, said peak corresponding to a centre positionwhere said first basis pattern was embedded into said image.
 29. Amethod as claimed in claim 28, comprising the further final step ofdecoding information from at least one of said parameters, said peakposition(s), an amplitude or relative phase of said peak(s).
 30. Amethod as claimed in claim 28, comprising the further initial step ofde-emphasising regions of said image having high signal variation.
 31. Amethod of adding registration marks to an image, said method compisingthe step of: maintaining at least one basis pattern, said basispattern(s) being formed substantially from a basis function, whereinsaid basis function is defined such that said basis function whencorrelated with a scaled and rotated version of said basis function issubstantially equal to the auto-correlation of said function within acomplex multiplicative constant; adding said basis pattern(s) to saidimage at at least tlree predetermined offsets relative to a center ofsaid image.
 32. A method as claimed in claim 31, wherein said at leastone basis pattern is a real function—substantially formed from saidbasis function.
 33. A method as claimed in claim 31 wherein said basisfunction is a function g(γ,θ) defined such that: g(γ,θ){circle over(x)}g(α.γ,θ+φ)=c.[g(γ,θ){circle over (x)}g(γ,θ)] wherein γ is adisplacement distance, θ and φ are angles, α is a positive real number,and c is a complex number not dependent on said displacement distance γnor said angle θ.
 34. A method as claimed in claim 31, wherein saidbasis function is a function g(γ,θ) defined such that: g(γ,θ){circleover (x)}N{g(α.γ,θ+φ)}=[g(γ,θ){circle over (x)}N{c.g(γ,θ)}] wherein Ndefines a real or imaginary component, γ is a displacement distance, θand φ are angles, α is a positive real number, and c is a complex numbernot dependent on said displacement distance γ nor said angle θ.
 35. Amethod as claimed in claim 31, wherein said basis function is of theform: g _(pmk)(γ,θ)=γ^(iαm+ρ)e^(ikθ), with n, k, p and α_(m) beingparameters of said basic function, and w_(n)(γ,θ) is a window function,wherein a real component of said basis patterns are added to said image.36. A method of registering a transformed image, wherein a first basispattern is embedded in said inage before transformation at at leastthree predetermined positions, said method comprising the steps of:maintaining a second basis pattern; detecting said first basis patternin said transformed image using said second basis pattern, said firstand second basis patterns being formed substantially from a basisfunction, wherein said basis function is defined such that said basisfunction when correlated with a scaled and rotated version of said basisfunction is substantially equal to the auto-correlation of said functionwithin a complex multiplicative constant; comparing positions of saidfirst pattern with said predetermined positions; determining lineartransformations for transforming said positions of said first patternwith said predetermined positions; and transforming said image to invertsaid linear transformations.
 37. A method as claimed in claim 36,wherein said at least one basis pattern is a real function—substantiallyformed from said basis function.
 38. A method as claimed in claim 36,wherein said basis function is a function g(γ,θ) defined such that:g(γ,θ){circle over (x)}g(α.γ,θ+φ)=c.[g(γ,θ){circle over (x)}g(γ,θ)]wherein γ is a displacement distance, θ and φ are angles, α is apositive real number, and c is a complex number not dependent on saiddisplacement distance γ nor said angle θ.
 39. A method as claimed inclaim 36, wherein said basis function is a function g(γ,θ) defined suchthat: g(γ,θ){circle over (x)}N{g(α.γ,θ+φ)}=[g(γ,θ){circle over(x)}N{c.g(γ,θ)}] wherein N defines a real or imaginary component, γ is adisplacement distance, θ and φ are angles, α is a positive real number,and c is a complex number not dependent on said displacement distance γnor said angle θ.
 40. A method as claimed in claim 36, wherein saidbasis function is of the form: g _(pmk)(γ,θ)=γ^(iαm+ρ)e^(ik0), with k, pand α_(m) being parameters of said basis function.
 41. A method asclaimed in claim 36, wherein said basis pattern is of the form: g_(pmkn)(γ,θ)=R{w _(n)(γ,θ).γ^(iαm+ρ)e^(ikθ)} with k, p and α_(m) beingparameters of said basis function, and w_(n)(γ,θ) is a window function,wherein a real component of said basis pattern is added to said image.42. A method as claimed in claim 36, wherein said detection stepcomprises the steps of: correlating said transformed image with saidsecond pattern to form a correlation image; and locating at least threemagnitude peaks in said correlation image said peaks determining thepositions of said first basis pattern in said transformed image.
 43. Amethod of embedding a watermark into an audio stream, said methodcomprising the step of: maintaining at least one basis pattern; andadding said basis pattern(s) to said audio stream, said basis pattern(s)being formed substantially from a basis function, wherein said basisfunction is defined such that said basis function when correlated with ascaled version of said basis function is substantially equal to theauto-correlation of said function within a complex multiplicativeconstant.
 44. A method as claimed in claim 43, wherein said at least onebasis pattern is a real function—substantially formed from said basisfunction.
 45. A method as claimed in claim 43, wherein said basisfunction is a function g(t) defined such that: g(t){circle over(x)}g(αt)=c.[g(t){circle over (x)}g(t)] wherein t is a displacementtime, α is a positive real number, and c is a complex number notdependent on said displacement time t.
 46. A method as claimed in claim43, wherein said basis function is a function g(t) defined such that:g(t){circle over (x)}N{g(αt)}=[g(t){circle over (x)}N{c.g(t)}] wherein Xdefines a real or imaginary component, t is a displacement time, α is apositive real number, and c is a complex number not dependent on saiddisplacement time t.
 47. A method as claimed in claim 43, wherein saidbasis function is of the form: g _(pm)(t)=t^(iαm+ρ), with p and α_(m)being parameters of said basis function.
 48. A method as claimed inclaim 43, wherein said basis pattern is of the form: g _(pmn)(t)=R{w_(n)(t)t ^(iαm+ρ)} with p and α_(m) being parameters of said basisfunction, and w_(n)(t) is a window function, wherein a real component ofsaid basis pattern is added to said audio stream.
 49. A method asclaimed in claim 48 wherein said window function w_(n)(t) removes orde-emphasises a region of said basis function having frequencies above apredetermined frequency.
 50. A method as claimed in claim 48 whereinsaid window function w_(n)(t) de-emphasises regions of said basisfunction corresponding with regions of said audio stream having a lowsignal variation.
 51. A method of detecting a watermark from an audiostream, said watermark having a first basis pattern embedded, saidmethod comprising the steps of: maintaining a second basis pattern; anddetecting said first basis pattern in said audio stream using saidsecond basis pattern, said first and second basis patterns being formedsubstantially from a basis function, wherein said basis function isdefined such that said basis function when correlated with a scaledversion of said basis function is substantially equal to theauto-correlation of said function within a complex multiplicativeconstant.
 52. A method as claimed in claim 51, wherein said at least onebasis pattern is a real function—substantially formed from said basisfunction.
 53. A method as claimed in claim 51, wherein said basisfunction is a function g(t) defined such that: g(t){circle over(x)}g(αt)=c.[g(t){circle over (x)}g(t)] wherein t is a displacementtime, α is a positive real number, and c is a complex number notdependent on said displacement time t.
 54. A method as claimed in claim51, wherein said basis function is a function g(t) defined such that:g(t){circle over (x)}N{g(αt)}=[g(t){circle over (x)}N{c.g(t)}] wherein Ndefines a real or imaginary component, t is a displacement time, α is apositive real number, and c is a complex number not dependent on saiddisplacement time t.
 55. A method as claimed in claim 51, wherein saidbasis function is of the form: g _(pm)(t)=t ^(iαm+ρ), with p and α_(m)being parameters of said basis function.
 56. A mnethod as claimed inclaim 51, wherein said basis pattern is of the form: g _(pmn)(t)=R{w_(n)(t)t ^(iαm+ρ)} with p and α_(m) being parameters of said basisfunction, and w_(n)(t) is a window function, wherein a real component ofsaid basis pattern is added to said audio stream.
 57. A method asclaimed in claim 51, wherein said detection step comprises the steps of:correlating said audio stream with said second pattern to form acorrelation signal; and locating at least one magnitude peak in saidcorrelation signal, said peak corresponding to a position where saidfirst basis pattern was embedded into said audio stream.
 58. A method asclaimed in claim 56, comprising the further initial step ofde-emphasising regions of said audio stream having high signalvariation.
 59. An image processing apparatus for embedding a watermarkinto an image, said apparatus comprising: means for maintaining at leastone basis pattern; and means for adding said basis pattern(s) to saidimage, said basis pattern(s) being formed substantially from a basisfunction, wherein said basis function is defined such that said basisfunction when correlated with a scaled and rotated version of said basisfunction is substantially equal to the auto-correlation of said functionwithin a complex multiplicative constant.
 60. An apparatus as claimed inclaim 59, wherein said at least one basis pattern is a realfunction—substantially formed from said basis function.
 61. An apparatusas claimed in claim 59, wherein said basis function is a function g(γ,θ)defined such that: g(γ,θ){circle over (x)}g(α.γ, θ+φ)=c.[g(γ,θ){circleover (x)}g(γ,θ)] wherein γ is a displacement distance, θ and φ areangles, α is a positive real number, and c is a complex number notdependent on said displacement distance γ nor said angle θ.
 62. Anapparatus as claimed in claim 59, wherein said basis function is afunction g(γ,θ) further defined such that: g(γ,θ){circle over(x)}N{g(α.γ,θ+φ)}[g(γ,θ){circle over (x)}N{c.g(γ,θ)}] wherein N definesa real or imaginary component, γ is a displacement distance, θ and φ areangles, α is a positive real number, and c is a complex number notdependent on said displacement distance γ nor said angle θ.
 63. Anapparatus as claimed in claim 59, wherein said basis function is of theform: g _(pmk)(γ,θ)=γ^(iαm+ρ)e^(ikθ), with k, p and α_(m) beingparameters of said basis function.
 64. An apparatus as claimed in claim59, wherein said basis pattern is of the form: g _(pmkn)(γ,θ)=R{w_(n)(γ,θ).γ^(iαm+ρ)e^(ikθ)} with k, p and α_(m) being parameters of saidbasis function, and w_(n)(γ,θ) is a window function, wherein a realcomponent of said basis pattern is added to said image.
 65. An apparatusas claimed in claim 64 wherein said window function w_(n)(γ,θ) removesor de-emphasises a central region of said basis function havingfrequencies above a predetermined frequency.
 66. An apparatus as claimedin claim 64 wherein said window function w_(n)(γ,θ) de-emphasisesregions of said basis function corresponding with regions of said imagehaving a low signal variation.
 67. An apparatus as claimed in claim 64wherein said window function w_(n)(γ,θ) contains a constant phasefactor.
 68. An apparatus as claimed in claim 63, wherein at least afirst and a second basis patterns are added to said image, with saidfirst and second basis patterns formed from a first and a second basisfunction respectively, and with at least one parameter k or α_(m) ofsaid first basis function being different to that of said second basisfunction.
 69. An apparatus as claimed in claim 63, wherein a pluralityof basis patterns are added with different offsets relative to a centerof said image.
 70. An apparatus as claimed in claim 69 furthercomprising means for encoding information into at least one of saidparameters, said offset, an amplitude or a relative phase added to saidbasis pattern.
 71. An image processing apparatus for embedding awatermark into an image, said apparatus comprising: means formaintaining at least one basis pattern; and means for adding said basispattern(s) to said image, wherein said basis pattern(s) is formnedsubstantially from a real component of a basis function, said basisfunction is of the form: s_(t,m)(x,y)=w(x,y)|x′| ^(iαl+ρx) |y′|^(iαm+ρy), wherein p_(x), p_(y), α_(l) and α_(m) are parameters of saidbasic function, w(γ,θ) is a window function, and x′ and y′ arepredetermined co-ordinates which are rotated relative to the Cartesianco-ordinates x and y.
 72. An image processing apparatus for embedding awatermark into an image, said apparatus comprising: means formaintaining at least one basis pattern; and means for adding said basispattern(s) to said image, said basis pattern(s) being formedsubstantially from a basis function, wherein said basis function isdefined such that said basis function when correlated with a scaledversion of said basis function is substantially equal to theauto-correlation of said function within a complex multiplicativeconstant.
 73. An apparatus as claimed in claim 72, wherein said basispattern(s) is a real function—substantially formed from said basisfunction.
 74. An apparatus as claimed in claim 72, wherein said basisfunction is a function g(γ,θ) defined such that: g(γ,θ){circle over(x)}g(α.γ,θ)=c.[g(γ,θ){circle over (x)}g(γ,θ)] wherein γ is adisplacement distance, θ is an angle, α is a positive real number, and cis a complex number not dependent on said displacement distance γ norsaid angle θ.
 75. An apparatus as claimed in claim 72, wherein saidbasis function is a function g(γ,θ) further defined such that:g(γ,θ){circle over (x)}N{g(α.γ,θ)}=[g(γ,θ){circle over (x)}N{c.g(γ,θ)}]wherein N defines a real or imaginary component, γ is a displacementdistance, θ is an angle, α is a positive real number, and c is a complexnumber not dependent on said displacement distance γ nor said angle θ.76. An image processing apparatus for embedding a watermark into animage, said apparatus comprising: means for maintaining at least onebasis pattern; and means for adding said basis pattern(s) to said image,said basis pattern(s) being formed substantially from a basis function,wherein said basis function is defined such that said basis functionwhen correlated with a rotated version of said basis function issubstantially equal to the auto-correlation of said function within acomplex multiplicative constant.
 77. An apparatus as claimed in claim76, wherein said basis pattern(s) is a real function—substantiallyformed from said basis function.
 78. An apparatus as claimed in claim77, wherein said basis function is a function g(γ,θ) defined such that:g(γ,θ){circle over (x)}g(γ,θ+φ)=c.[g(γ,θ){circle over (x)}g(γ,θ)]wherein γ is a displacement distance, θ and φ are angles, α is apositive real number, and c is a complex number not dependent on saiddisplacement distance γ nor said angle θ.
 79. An apparatus as claimed inclaim 77, wherein said basis function is a function g(γ,θ) furtherdefined such that: g(γ,θ){circle over (x)}N{g(γ,θ+φ)}=[g(γ,θ){circleover (x)}N{c(γ,θ)}] wherein N defines a real or imaginary component, γis a displacement distance, θ and φ are angles, and c is a complexnumber not dependent on said displacement distance γ nor said angle θ.80. An image processing apparatus for detecting a watermark from animage, said watermark having a first basis pattern embedded, saidapparatus comprising: means for maintaining a second basis pattern; andmeans for detecting said first basis pattern in said image using saidsecond basis pattern, said first and second basis patterns being formedsubstantially from a basis function, wherein said basis function isdefined such that said basis function when correlated with a scaled androtated version of said basis function is substantially equal to theauto-correlation of said function within a complex multiplicativeconstant.
 81. An apparatus as claimed in claim 80, wherein said at leastone basis pattern is a real function—substantially formed from saidbasis function.
 82. An apparatus as claimed in claim 80, wherein saidbasis function is a function g(γ,θ) defined such that: g(γ,θ){circleover (x)}g(α.γ,θ+φ)=c.[g(γ,θ){circle over (x)}g(γ,θ)] wherein γ is adisplacement distance, θ and φ are angles, α is a positive real nunber,and c is a complex number not dependent on said displacement distance γnor said angle θ.
 83. An apparatus as claimed in claim 80, wherein saidbasis function is a function g(γ,θ) defined such that: g(γ,θ){circleover (x)}{g(α.γ,θ+φ)}=[g(γ,θ){circle over (x)}N{c.g(γ,θ)}] wherein Ndefines a real or imaginary component, γ is a displacement distance, θand φ are angles, α is a positive real number, and c is a complex numbernot dependent on said displacement distance γ nor said angle θ.
 84. Anapparatus as claimed in claim 80, wherein said basis function is of theform: g _(pmk)(γ,θ)=γ^(iαm+ρ)e^(ik0), with k, p and α_(m) beingparameters of said basis function.
 85. An apparatus as claimed in claim80, wherein said basis pattern is of the form: g _(pmkn)(γ,θ)=R{w_(n)(γ,θ).γ^(iαm+ρ)e^(ikθ)} with k, p and α_(m) being parameters of saidbasis function, and w_(n)(γ,θ) is a window function, wherein a realcomponent of said basis pattern is added to said image.
 86. An apparatusas claimed in claim 80, wherein said means for detection comprises:means for correlating said image with said second pattern to form acorrelation image; and means for locating at least one magnitude peak insaid correlation image, said peak corresponding to a centre positionwhere said first basis pattern was embedded into said image.
 87. Animage processing apparatus for adding registration marks to an image,said apparatus comprising: means for maintaining at least one basispattern, said basis pattern(s) being formed substantially from a basisfunction, wherein said basis function is defined such that said basisfunction when correlated with a scaled and rotated version of said basisfunction is substantially equal to the auto-correlation of said functionwithin a complex multiplicative constant; means for adding said basispattern(s) to said image at at least three predetermined offsetsrelative to a center of said image.
 88. An apparatus as claimed in claim87, wherein said at least one basis pattern is a realfunction—substantially formed from said basis function.
 89. An apparatusas claimed in claim 87 wherein said basis function is a function g(γ,θ)defined such that: g(γ,θ){circle over (x)}g(α.γ,θ+φ)=c.[g(γ,θ){circleover (x)}g(γ,θ)] wherein γ is a displacement distance, θ and φ areangles, α is a positive real number, and c is a complex number notdependent on said displacement distance γ nor said angle θ.
 90. Anapparatus as claimed in claim 87, wherein said basis function is afunction g(γ,θ) defined such that: g(γ,θ){circle over(x)}N{g(α.γ,θ+φ)}=[g(γ,θ){circle over (x)}N{c.g(γ,θ)}] wherein N definesa real or imaginary component, γ is a displacement distance, θ and φ areangles, α is a positive real number, and c is a complex number notdependent on said displacement distance γ nor said angle θ.
 91. Anapparatus as claimed in claim 87, wherein said basis function is of theform: g _(pmk)(γ,θ)=γ^(iαm+ρ) e ^(ikθ), with n, k, p and α_(m) beingparameters of said basic function, and w_(n)(γ,θ) is a window function,wherein a real component of said basis patterns are added to said image.92. An image processing apparatus for registering a transformed image,wherein a first basis pattern is embedded in said image beforetransformation at at least three predetermined positions, said apparatuscomprising: means for maintaining a second basis pattern; means fordetecting said first basis pattern in said transformed image using saidsecond basis pattern, said first and second basis patterns being formedsubstantially from a basis function, wherein said basis function isdefined such that said basis function when correlated with a scaled androtated version of said basis function is substantially equal to theauto-correlation of said function within a complex multiplicativeconstant; means for comparing positions of said first pattern with saidpredetermined positions; means for determining linear transformationsfor transforming said positions of said first pattern with saidpredetermined positions; and means for transforming said image to invertsaid linear transformations.
 93. An apparatus as claimed in claim 92,wherein said at least one basis pattern is a real function—substantiallyformed from said basis function.
 94. An apparatus as claimed in claim92, wherein said basis function is a function g(γ,θ) defined such that:g(γ,θ){circle over (x)}g(α.γ,θ+φ)=c.[g(γ,θ){circle over (x)}g(γ,θ)]wherein γ is a displacement distance, θ and φ are angles, α is apositive real number, and c is a complex number not dependent on saiddisplacement distance γ nor said angle θ.
 95. An apparatus as claimed inclaim 92, wherein said basis function is a function g(γ,θ) defined suchthat: g(γ,θ){circle over (x)}N{g(α.γ,θ+φ)}=[g(γ,θ){circle over(x)}N{c.g(γ,θ)}] wherein N defines a real or imaginary component, γ is adisplacement distance, θ and φ are angles, α is a positive real number,and c is a complex number not dependent on said displacement distance γnor said angle θ.
 96. An apparatus as claimed in claim 92, wherein saidbasis function is of the form: g _(pmk)(γ,θ)=γ^(iαm+ρ) e ^(ikθ), with k,p and α_(m) being parameters of said basis function.
 97. An apparatus asclaimed in claim 92, wherein said basis pattern is of the form: g_(pmkn)(γ,θ)=R{w _(n)(γ,θ).γ^(iαm+ρ) e ^(ikθ)} with k, p and α_(m) beingparameters of said basis function, and w_(n)(γ,θ) is a window function,wherein a real component of said basis pattern is added to said image.98. An apparatus as claimed in claim 92, wherein said means fordetection comprises: means for correlating said transformed image withsaid second pattern to form a correlation image; and means for locatingat least three magnitude peaks in said correlation image, said peaksdetermining the positions of said first basis pattern in saidtransformed image.
 99. A data processing apparatus for embedding awatermark into an audio stream, said apparatus comprising: means formaintaining at least one basis pattern; and means for adding said basispattern(s) to said audio stream, said basis pattern(s) being formedsubstantially from a basis function, wherein said basis function isdefined such that said basis function when correlated with a scaledversion of said basis function is substantially equal to theauto-correlation of said function within a complex multiplicativeconstant.
 100. An apparatus as claimed in claim 99, wherein said atleast one basis pattern is a real function—substantially formed fromsaid basis function.
 101. An apparatus as claimed in claim 99, whereinsaid basis function is a function g(t) defined such that: g(t){circleover (x)}g(α.t)=c.[g(t){circle over (x)}g(t)] wherein t is adisplacement time, α is a positive real number, and c is a complexnumber not dependent on said displacement time γ.
 102. An apparatus asclaimed in claim 99, wherein said basis function is a function g(t)defined such that: g(t){circle over (x)}N{g(α.t)}=[g(t){circle over(x)}N{c.g(t)}] wherein N defines a real or imaginary component, t is adisplacement time, α is a positive real number, and c is a complexnumber not dependent on said displacement time t.
 103. An apparatus asclaimed in claims 99, wherein said basis function is of the form: g_(pm)(t)=t ^(iαm+ρ), with p and α_(m) being parameters of said basisfunction.
 104. An apparatus as claimed in claim 99, wherein said basispattern is of the form: g _(pmn)(t)=R{w _(n)(t)t ^(iαm+])} with p andα_(m) being parameters of said basis function, and w_(n)(t) is a windowfunction, wherein a real component of said basis pattern is added tosaid audio stream.
 105. An apparatus as claimed in claim 104 whereinsaid window function w_(n)(t) removes or de-emphasises a region of saidbasis function having frequencies above a predetermined frequency. 106.An apparatus as claimed in claim 104 wherein said window functionw_(n)(t) de-emphasises regions of sad basis function corresponding withregions of said audio stream having a low signal variation.
 107. A dataprocessing apparatus for detecting a watermark from an audio stream,said watermark having a first basis pattern embedded, said apparatuscomprising: means for maintaining a second basis pattern; and means fordetecting said first basis pattern in said audio stream using saidsecond basis pattern, said first and second basis patterns being formedsubstantially from a basis function, wherein said basis function isdefined such that said basis function when correlated with a scaledversion of said basis function is substantially equal to theauto-correlation of said function within a complex multiplicativeconstant.
 108. An apparatus as claimed in claim 107, wherein said atleast one basis pattern is a real function—substantially formed fromsaid basis function.
 109. An apparatus as claimed in claim 107, whereinsaid basis function is a function g(t) defined such that: g(t){circleover (x)}g(α.t)=c.[g(t){circle over (x)}g(t)] wherein t is adisplacement time, α is a positive real number, and c is a complexnumber not dependent on said displacement time t.
 110. An apparatus asclaimed in claim 107, wherein said basis function is a function g(t)defined such that: g(t){circle over (x)}N{g(α.t)}=[g(t){circle over(x)}N{c.g(t)}] wherein N defines a real or imaginary component, t is adisplacement time, α is a positive real number, and c is a complexnumber not dependent on said displacement time t.
 111. An apparatus asclaimed in claim 107, wherein said basis function is of the form: g_(pm)(t)=t ^(iαm+ρ), with p and α_(m) being parameters of said basisfunction.
 112. An apparatus as claimed in claim 107, wherein said basispattern is of the form: g _(pmn)(t)=R{w _(n)(t)t ^(iαm+ρ)} with p andα_(m) being parameters of said basis function, and w_(n)(t) is a windowfunction, wherein a real component of said basis pattern is added tosaid audio stream.
 113. An apparatus as claimed in claim 107, whereinsaid means for detection comprises: means for correlating said audiostream with said second pattern to form a correlation signal; and meansfor locating at least one magnitude peak in said correlation signal,said peak corresponding to a position where said first basis pattern wasembedded into said audio stream.
 114. A program stored in a memorymedium for embedding a watermark into an image, said program comprising:code for maintaining at least one basis pattern; and code for addingsaid basis pattern(s) to said image, wherein said basis pattern(s) isformed substantially from a basis function, said basis function beingdefined such that said basis function when correlated with a scaled androtated version of said basis function is substantially equal to theauto-correlation of said function within a complex multiplicativeconstant.
 115. A program as claimed in claim 114, wherein said at leastone basis pattern is a real function—substantially formed from saidbasis function.
 116. A program as claimed in claim 114, wherein saidbasis function is a function g(γ,θ) defined such that: g(γ,θ){circleover (x)}g(α.γ,θ+φ)=c.[g(γ,θ){circle over (x)}g(γ,θ)] wherein γ is adisplacement distance, θ and φ are angles, α is a positive real number,and c is a complex number not dependent on said displacement distance γnor said angle θ.
 117. A program as claimed in claim 114, wherein saidbasis function is a function g(γ,θ) defined such that: g(γ,θ){circleover (x)}N{g(α.γ,θ+φ)}=[g(γ,θ){circle over (x)}N{c.g(γ,θ)}] wherein Ndefines a real or imaginary component, γ is a displacement distance, θand φ are angles, α is a positive real number, and c is a complex numbernot dependent on said displacement distance γ nor said angle θ.
 118. Aprogram as claimed in claim 114, wherein said basis function is of theform: wherein said basis function is a function g(γ,θ) further definedsuch that: g(γ,θ){circle over (x)}N{g(α.γ,θ+φ)}=[g(γ,θ){circle over(x)}N{c.g(γ,θ)}] wherein N defines a real or imaginary component, γ is adisplacement distance, θ and φ are angles, α is a positive real number,and c is a complex number not dependent on said displacement distance γnor said angle θ.
 119. A program as claimed in claim 114, wherein aplurality of basis patterns are added with different offsets relative toa center of said image.
 120. A program stored in a memory medium fordetecting a watermark from an image, said watermark having a first basispattern embedded, said program comprising: code for maintaining a secondbasis pattern; and code for detecting said first basis pattern in saidimage using said second basis pattern, wherein said first and secondbasis patterns are formed substantially from a basis function, saidbasis function being defined such that said basis function whencorrelated with a scaled and rotated version of said basis function issubstantially equal to the auto-correlation of said function within acomplex multiplicative constant.
 121. A program as claimed in claim 120,wherein said at least one basis pattern is a real function—substantiallyformed from said basis function.
 122. A program as claimed in claim 120,wherein said basis function is a function g(γ,θ) defined such that:g(γ,θ){circle over (x)}g(α.γ,θ+φ)=c.[g(γ,θ){circle over (x)}g(γ,θ)]wherein γ is a displacement distance, θ and φ are angles, α is apositive real number, and c is a complex number not dependent on saiddisplacement distance γ nor said angle θ.
 123. A program as claimed inclaim 120, wherein said basis function is a function g(γ,θ) defined suchthat: g(γ,θ){circle over (x)}N{g(α.γ,θ+φ)}=[g(γ,θ){circle over(x)}N{c.g(γ,θ)}] wherein N defines a real or imaginary component, γ is adisplacement distance, θ and φ are angles, α is a positive real number,and c is a complex number not dependent on said displacement distance γnor said angle θ.
 124. A program as claimed in claim 120, wherein saidbasis function is of the form: g_(pmk)(γ,θ)=γ^(iαm+ρ) e ^(ikθ), with k,p and α_(m) being parameters of said basis function.
 125. A program asclaimed in claim 120, wherein said basis pattern is of the form: g_(pmkn)(γ,θ)=R{w _(n)(γ,θ).γ^(iαm+ρ) e ^(ikθ)} with k, p and α_(m) beingparameters of said basis function, and w_(n)(γ,θ) is a window function,wherein a real component of said basis pattern is added to said image.126. A program as claimed in claim 120, wherein said code for detectioncomprises: code for correlating said image with said second pattern toform a correlation image; and code for locating at least one magnitudepeak in said correlation image, said peak corresponding to a centreposition where said first basis pattern was embedded into said image.127. A program stored in a memory medium for adding registration marksto an image, said program comprising: code for maintaining at least onebasis pattern, wherein said basis pattern(s) is formed substantiallyfrom a basis function, said basis function being defined such that saidbasis function when correlated with a scaled and rotated version of saidbasis function is substantially equal to the auto-correlation of saidfunction within a complex multiplicative constant; code for adding saidbasis pattern(s) to said image at at least three predetermined offsetsrelative to a center of said image.
 128. A program stored in a memorymedium for registering a transformed image, wherein a first basispattern is embedded in said image before transformation at at leastthree predetermined positions, said program comprising: code formaintaining a second basis pattern; code for detecting said first basispattern in said transformed image using said second basis pattern,wherein said first and second basis patterns are formed substantiallyfrom a basis function, said basis function being defined such that saidbasis function when correlated with a scaled and rotated version of saidbasis function is substantially equal to the auto-correlation of saidfunction within a complex multiplicative constant; code for comparingpositions of said first pattern with said predetermined positions; codefor determining linear transformations for transforming said positionsof said first pattern with said predetermined positions; and code fortransforming said image to invert said linear transformations.
 129. Aprogram as claimed in claim 128, wherein said code for detectioncomprises: code for correlating said transformed image with said secondpattern to form a correlation image; and code for locating at leastthree magnitude peaks in said correlation image, said peaks determiningthe positions of said first basis pattern in said transformed image.130. A program stored in a memory medium for embedding a watermark intoan audio stream, said program comprising: code for maintaining at leastone basis pattern; and code for adding said basis pattern(s) to saidaudio stream, wherein said basis pattern(s) is formed substantially froma basis function, said basis function being defined such that said basisfunction when correlated with a scaled version of said basis function issubstantially equal to the auto-correlation of said function within acomplex multiplicative constant.
 131. A program stored in a memorymedium for detecting a watermark from an audio stream, said watermarkhaving a first basis pattern embedded, said program comprising: code formaintaining a second basis pattern; and code for detecting said firstbasis pattern in said audio stream using said second basis pattern,wherein said first and second basis patterns are formed substantiallyfrom a basis function, said basis function being defined such that saidbasis function when correlated with a scaled version of said basisfunction is substantially equal to the auto-correlation of said functionwithin a complex multiplicative constant.
 132. A program as claimed inclaims 131, wherein said code for detection comprises: code forcorrelating said audio stream with said second pattern to form acorrelation signal; and code for locating at least one magnitude peak insaid correlation signal, said peak corresponding to a position wheresaid first basis pattern was embedded into said audio stream.
 133. Awatermarked image comprising: an original image; and one or more basispatterns added to said original image, wherein said basis pattern(s) isformed substantially from a basis function, said basis function beingdefined such that said basis function when correlated with a scaled androtated version of said basis function is substantially equal to theauto-correlation of said function within a complex multiplicativeconstant.
 134. An image as claimed in claim 133, wherein said at leastone basis pattern is a real function—substantially formed from saidbasis function.
 135. An image as claimed in claim 133, wherein saidbasis function is of the form: g _(pmk)(γ,θ)=γ^(iαm+p) e ^(ikθ), with k,p and α_(m) being parameters of said basis function.
 136. An image asclaimed in claim 133, wherein said basis pattern is of the form: g_(pmkn)(γ,θ)=R{w _(n)(γ,θ).γ^(iαm+ρ) e ^(ikθ)} with k, p and α_(m) beingparameters of said basis function, and w_(n)(γ,θ) is a window function,wherein a real component of said basis pattern is added to said image.137. An audio stream comprising: an original audio stream; and one ormore basis patterns added to said audio stream, wherein said basispattern(s) is formed substantially from a basis function, said basisfunction being defined such that said basis function when correlatedwith a scaled version of said basis function is substantially equal tothe auto-correlation of said function within a complex multiplicativeconstant.
 138. An audio stream as claimed in claim 137, wherein said atleast one basis pattern is a real function—substantially formed fromsaid basis function.
 139. An audio stream as claimed in claim 137,wherein said basis function is of the form: g _(pm)(t)=t ^(iαm+ρ), withp and α_(m) being parameters of said basis function.
 140. An audiostream as claimed in claim 139, wherein said basis pattern is of theform: g _(pmn)(t)=R{w _(n)(t)t ^(iαm+ρ)} with p and α_(m) beingparameters of said basis function, and w_(n)(t) is a window function,wherein a real component of said basis pattern is added to said audiostream.